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Browning was "PVS".

Yes, she was diagnosed PVS by at least one doctor. Nevertheless, I have my doubts, and you seem to doubt the diagnosis also.

From Browning:

At the same time, the medical evidence reflected that Mrs. Browning was not comatose. Although she was noncommunicative, she "appeared alert and would follow [a visitor] with her eyes."

That's why I asserted that she was not PVS, but after reading the case again, Browning quotes a doctor claiming that she was PVS by his definition:

Dr. Barnhill opined that she was in a persistent vegetative state, which he defined as the absence of cognitive behavior and inability to communicate or interact purposefully with the environment.

Nevertheless, being diagnosed PVS is not a requirement to refuse artificial life support. For instance, Mrs. Wons was not terminally ill, except for the fact that she refused medical treatment:

Norma Wons entered Jackson Memorial Hospital, a medical facility operated by the Public Health Trust of Dade County, with a condition known as dysfunctional uterine bleeding. Doctors informed Mrs. Wons that she would require treatment in the form of a blood transfusion or she would, in all probability, die. [...]
Nevertheless, the court granted the petition, ordering the hospital doctors to administer the blood transfusion, which was done while Mrs. Wons was unconscious. The trial judge reasoned that minor children have a right to be reared by two loving parents, a right which overrides the mother's rights of free religious exercise and privacy. Upon regaining consciousness, Mrs. Wons appealed to the third district which reversed the order

Referring to Wons, the Court ruled in Browning that any competent person can refuse life-saving medical treatment:

We held that a competent, thirty-eight-year-old practicing Jehovah's Witness could exercise her constitutional right to refuse an emergency blood transfusion, without which her death was certain to follow shortly. We approved the opinion of the district court, which concluded that Mrs. Wons was entitled "to exercise her religious freedom and to lead her private life according to her own conscience."

And if you had any doubts whether feeding tubes are artificial life support, the Court continued:

We conclude that a competent person has the constitutional right to choose or refuse medical treatment, and that right extends to all relevant decisions concerning one's health. Courts overwhelmingly have held that a person may refuse or remove artificial life-support, whether supplying oxygen by a mechanical respirator or supplying food and water through a feeding tube. We agree and find no significant legal distinction between these artificial means of life-support.

And any claim that a written directive was required in Browning is rejected by the Court.

Oral declarations are enough:

Although a surrogate may rely on oral statements made by the incompetent, while competent, to exercise the incompetent's wishes to forego life-sustaining treatment, the presumption of clear and convincing evidence that attaches to a written declaration does not attach to purely oral declarations. Oral evidence, considered alone, may constitute clear and convincing evidence. However, the surrogate would bear the burden of proof if a decision based on purely oral evidence is challenged.